This paper here goes into some detail about how Mars' experiences its own form of 'ice ages' on a quasi periodic basis driven by the wobbling of its axis. The main mechanism outlined is that the stability of water ice on the surface increases with increased obliquity. Why is this?

On a more discussion based addition to the question, could factors such as ice albedo and other feedback loops play a similar role in Mars' ice ages that they do in Earth's ice ages?

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Not sure of what it is you are asking here.The polor caps are formed due to relativity humidity of thin atmosphere at freezing point forming "air Bourne" crystals and fall to the ground.this occurs as "furring" on already frozen twigs and branches here on earth.
The furring can also evaporate(dissapear)without turing to water if the air is dry.
Earth ice age could be due long term " Sun" orbit which is changing as it revolves around "milky way" but due to the earths rotation(gyroscope effect) could be,say,45deg tilt relative to the change in new sun galaxy orbit.Just a thought,no theory reference.